cmd/compile: derive bounds on signed %N for N a power of 2

-N+1 <= x % N <= N-1

This is useful for cases like:

func setBit(b []byte, i int) {
    b[i/8] |= 1<<(i%8)
}

The shift does not need protection against larger-than-7 cases.
(It does still need protection against <0 cases.)

Change-Id: Idf83101386af538548bfeb6e2928cea855610ce2
Reviewed-on: https://go-review.googlesource.com/c/go/+/672995
Reviewed-by: Jorropo <jorropo.pgm@gmail.com>
Reviewed-by: David Chase <drchase@google.com>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>
Reviewed-by: Michael Knyszek <mknyszek@google.com>

src/cmd/compile/internal/ssa/prove.go

@@ -1757,7 +1757,9 @@ func (ft *factsTable) flowLimit(v *Value) bool {
 	case OpSub64, OpSub32, OpSub16, OpSub8:
 		a := ft.limits[v.Args[0].ID]
 		b := ft.limits[v.Args[1].ID]
-		return ft.newLimit(v, a.sub(b, uint(v.Type.Size())*8))
+		sub := ft.newLimit(v, a.sub(b, uint(v.Type.Size())*8))
+		mod := ft.detectSignedMod(v)
+		return sub || mod
 	case OpNeg64, OpNeg32, OpNeg16, OpNeg8:
 		a := ft.limits[v.Args[0].ID]
 		bitsize := uint(v.Type.Size()) * 8
@@ -1913,6 +1915,122 @@ func (ft *factsTable) flowLimit(v *Value) bool {
 	return false
 }
 
+// See if we can get any facts because v is the result of signed mod by a constant.
+// The mod operation has already been rewritten, so we have to try and reconstruct it.
+//   x % d
+// is rewritten as
+//   x - (x / d) * d
+// furthermore, the divide itself gets rewritten. If d is a power of 2 (d == 1<<k), we do
+//   (x / d) * d = ((x + adj) >> k) << k
+//               = (x + adj) & (-1<<k)
+// with adj being an adjustment in case x is negative (see below).
+// if d is not a power of 2, we do
+//   x / d = ... TODO ...
+func (ft *factsTable) detectSignedMod(v *Value) bool {
+	if ft.detectSignedModByPowerOfTwo(v) {
+		return true
+	}
+	// TODO: non-powers-of-2
+	return false
+}
+func (ft *factsTable) detectSignedModByPowerOfTwo(v *Value) bool {
+	// We're looking for:
+	//
+	//   x % d ==
+	//   x - (x / d) * d
+	//
+	// which for d a power of 2, d == 1<<k, is done as
+	//
+	//   x - ((x + (x>>(w-1))>>>(w-k)) & (-1<<k))
+	//
+	// w = bit width of x.
+	// (>> = signed shift, >>> = unsigned shift).
+	// See ./_gen/generic.rules, search for "Signed divide by power of 2".
+
+	var w int64
+	var addOp, andOp, constOp, sshiftOp, ushiftOp Op
+	switch v.Op {
+	case OpSub64:
+		w = 64
+		addOp = OpAdd64
+		andOp = OpAnd64
+		constOp = OpConst64
+		sshiftOp = OpRsh64x64
+		ushiftOp = OpRsh64Ux64
+	case OpSub32:
+		w = 32
+		addOp = OpAdd32
+		andOp = OpAnd32
+		constOp = OpConst32
+		sshiftOp = OpRsh32x64
+		ushiftOp = OpRsh32Ux64
+	case OpSub16:
+		w = 16
+		addOp = OpAdd16
+		andOp = OpAnd16
+		constOp = OpConst16
+		sshiftOp = OpRsh16x64
+		ushiftOp = OpRsh16Ux64
+	case OpSub8:
+		w = 8
+		addOp = OpAdd8
+		andOp = OpAnd8
+		constOp = OpConst8
+		sshiftOp = OpRsh8x64
+		ushiftOp = OpRsh8Ux64
+	default:
+		return false
+	}
+
+	x := v.Args[0]
+	and := v.Args[1]
+	if and.Op != andOp {
+		return false
+	}
+	var add, mask *Value
+	if and.Args[0].Op == addOp && and.Args[1].Op == constOp {
+		add = and.Args[0]
+		mask = and.Args[1]
+	} else if and.Args[1].Op == addOp && and.Args[0].Op == constOp {
+		add = and.Args[1]
+		mask = and.Args[0]
+	} else {
+		return false
+	}
+	var ushift *Value
+	if add.Args[0] == x {
+		ushift = add.Args[1]
+	} else if add.Args[1] == x {
+		ushift = add.Args[0]
+	} else {
+		return false
+	}
+	if ushift.Op != ushiftOp {
+		return false
+	}
+	if ushift.Args[1].Op != OpConst64 {
+		return false
+	}
+	k := w - ushift.Args[1].AuxInt // Now we know k!
+	d := int64(1) << k             // divisor
+	sshift := ushift.Args[0]
+	if sshift.Op != sshiftOp {
+		return false
+	}
+	if sshift.Args[0] != x {
+		return false
+	}
+	if sshift.Args[1].Op != OpConst64 || sshift.Args[1].AuxInt != w-1 {
+		return false
+	}
+	if mask.AuxInt != -d {
+		return false
+	}
+
+	// All looks ok. x % d is at most +/- d-1.
+	return ft.signedMinMax(v, -d+1, d-1)
+}
+
 // getBranch returns the range restrictions added by p
 // when reaching b. p is the immediate dominator of b.
 func getBranch(sdom SparseTree, p *Block, b *Block) branch {

test/codegen/shift.go

@@ -656,3 +656,12 @@ func rsh64to8(v int64) int8 {
 	}
 	return x
 }
+
+// We don't need to worry about shifting
+// more than the type size.
+// (There is still a negative shift test, but
+// no shift-too-big test.)
+func signedModShift(i int) int64 {
+	// arm64:-"CMP",-"CSEL"
+	return 1 << (i % 64)
+}